"A product of painstaking negotiation and compromise, the BBA established a bipartisan framework for Congress to move forward on annual funding bills based on the principles of full and fairly allocated funding, a rejection of poison pill riders, and parity between the Pentagon’s needs and other needs here at home," they wrote in the letter released Monday.

They added that because of the deal, senators can start work on individual appropriations bills without waiting for the Senate to pass another budget.

McConnell said that he was "glad" that Democrats supported moving the appropriations bills quickly.

"Earlier this year, I asked the Appropriations Committee to accelerate their work so that we can be ready to consider individual bills as soon as mid-April," he added.

McConnell told reporters earlier this year that Republicans would make “a major effort” to pass a budget. The Senate Republican leader also spoke last week in a closed-door meeting with House Republicans, where he urged them to stand by last fall's agreement with President Obama.

House Republicans have been battling for weeks on a budget blueprint and are struggling to reach a consensus.

McConnell has repeatedly suggested that his top goal for 2016 is to pass the 12 individual spending bills through "regular order." Enzi on Monday argued that the Senate can pass appropriations bills even without a budget resolution because the top-line spending numbers were set in last year’s budget deal.

Top Democrats added in their letter that they support McConnell's strategy, calling it a "win-win," but warned that lawmakers will be in a "race against a Senate calendar that is unusually abbreviated."